This study aims to develop a new strategy for solving partial differential equations with fractional derivatives (FPDEs) using artificial neural networks (ANNs). Numerical solutions to FPDEs are obtained through the Hermite wavelet neural network (HWNN) model. The Caputo fractional derivative is consistently applied throughout the research to address fractional-order partial differential problems. To enhance computational efficiency and expand the input pattern, the hidden layer is removed. A neural network (NN) model featuring a feed-forward architecture and error-back propagation without supervision is employed to optimize network parameters and minimize errors. Numerical illustrations are presented to demonstrate the effectiveness of this approach in preserving computational efficiency while solving FPDEs.

中文翻译：

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使用 Hermite 小波人工神经网络数值求解分数偏微分方程的自适应算法


本研究旨在开发一种使用人工神经网络 (ANN) 求解具有分数阶导数的偏微分方程 (FPDE) 的新策略。 FPDE 的数值解是通过 Hermite 小波神经网络 (HWNN) 模型获得的。在整个研究中始终应用卡普托分数阶导数来解决分数阶偏微分问题。为了提高计算效率并扩展输入模式，隐藏层被删除。采用前馈架构和无监督误差反向传播的神经网络（NN）模型来优化网络参数并最小化误差。数值插图证明了该方法在求解 FPDE 时保持计算效率的有效性。